Related papers: Spatial correlations in nonequilibrium reaction-di…
This study handles spatial three-dimensional solution of the nonlinear diffusion equation without particular initial conditions. The functional behavior of the equation and the concentration have been studied in new ways. An auxiliary…
Spatial fields in the Earth and environmental sciences are often available at multiple scales or resolutions. While coarse-scale data (e.g., from global circulation models) are often abundant, they lack the local detail provided by…
Integro-differential equations, analyzed in this work, comprise an important class of models of continuum media with nonlocal interactions. Examples include peridynamics, population and opinion dynamics, the spread of disease models, and…
We establish a unified fluctuation-response relation for Langevin dynamics. By exploiting the common mathematical structures underlying fluctuations and responses of empirical density and current, we derive a unified identity that…
The paper treats a reaction-diffusion equation with hysteretic nonlinearity on a one-dimensional lattice. It arises as a result of the spatial discretization of the corresponding continuous model with so-called nontransverse initial data…
X-ray photon correlation spectroscopy (XPCS) is a powerful tool for the investigation of dynamics covering a broad range of time and length scales. The two-time correlation function (TTC) is commonly used to track non-equilibrium dynamical…
Stochastic chemical systems with diffusion are modeled with a reaction-diffusion master equation. On a macroscopic level, the governing equation is a reaction-diffusion equation for the averages of the chemical species. On a mesoscopic…
In coupled reaction-diffusion systems, modes with two different length scales can interact to produce a wide variety of spatiotemporal patterns. Three-wave interactions between these modes can explain the occurrence of spatially complex…
The correlation between the values of wavefunctions at two different spatial points is examined for chaotic systems with time-reversal symmetry. Employing a supermatrix method, we find that there exist long-range Friedel oscillations of the…
We present a theoretical study on pattern formation occurring in miscible fluids reacting by a second-order reaction $A + B \to S$ in a vertical Hele-Shaw cell under constant gravity. We have recently reported that concentration-dependent…
Viscoelastic subdiffusion governed by a fractional Langevin equation is studied numerically in a random Gaussian environment modeled by stationary Gaussian potentials with decaying spatial correlations. This anomalous diffusion is…
A new method is proposed to numerically extract the diffusivity of a (typically nonlinear) diffusion equation from underlying stochastic particle systems. The proposed strategy requires the system to be in local equilibrium and have…
A reaction--diffusion replicator equation is studied. A novel method to apply the principle of global regulation is used to write down the model with explicit spatial structure. Properties of stationary solutions together with their…
We construct solutions of nonlinear reaction-diffusion equations with nonlinear boundary conditions in spaces where the problem is supercritical and show the nonlinear balance required between the nonlinear terms in order to obtain a…
Quantum statistical correlations and momentum distributions are calculated for a spherically symmetric, three-dimensionally expanding finite fireballs, for non-relativistic expansions applying plane-wave approximation. The new concepts of…
We present an analytical closed form expression, which gives a good approximate propagator for diffusion on the sphere. Our formula is the spherical counterpart of the Gaussian propagator for diffusion on the plane. While the analytical…
High-dimensional fractional reaction-diffusion equations have numerous applications in the fields of biology, chemistry, and physics, and exhibit a range of rich phenomena. While classical algorithms have an exponential complexity in the…
The effective, fast transport of matter through porous media is often characterized by complex dispersion effects. To describe in mathematical terms such situations, instead of a simple macroscopic equation (as in the classical Darcy's…
We develop and implement new probabilistic strategy for proving basic results about long time behaviour for interacting diffusion processes on unbounded lattice. The concept of the solution used is rather weak as we construct the process as…
The spatial correlation function of the momentum density in the three-dimensional dilute sheared granular fluids is theoretically investigated. The existence of the long-range correlation is verified through both the analytic calculation…